The measurements of coexistence curves and turbidity for {xC6H5CN + (1  x)CH3(CH2)14CH3} in the critical region

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Abstract

The coexistence curves and turbidity data for a critical solution of (benzonitrile + hexadecane) have been reported. The critical amplitudes and exponents relating to the difference in density variables of two coexisting phases, the correlation length, and the osmotic compressibility have been calculated. The experimental results of the coexistence curves have also been analyzed to examine the Wegner correction terms and the behaviour of the diameter of the coexistence curves. A combination of the Wegner equation and the expression for the diameter has been used to describe successfully the coexistence curves.

Introduction

There exists an isolated critical solution point at the equilibrium vapour pressure in a binary liquid mixture. Near this critical point, the difference Δρ of a general density variable, between two coexistence phases, the correlation length ξ, and the osmotic compressibility χ exhibit universal power-law dependences on the reduced temperature t {t = |T  Tc|/Tc, where Tc is the critical temperature} near the critical point. These dependences may be described by the following forms:Δρ=ρ2-ρ1=Btβ,ξt-ν=ξ0t-ν,χt-γ=χ0t-γ,where ρ is the density variable, ρ1 and ρ2 are the values of the density variables in the upper and lower coexistence phases; β, ν, and γ are the critical exponents; B, ξ0, and χ0 are the critical amplitudes that are dependent on molecular mass of chain-molecule component for chain-molecule solutions of both small molecules and polymers [1]. As a continuing part of study of the critical phenomena of binary mixtures of chain molecules in a polar solvent, in this paper, we report the experimental results of the coexistence curves and the turbidity for the system of (benzonitrile + hexadecane). The results are analyzed to obtain the critical exponents and critical amplitudes corresponding to (ρ2  ρ1), ξ, and χ. The diameters ρd of the coexistence curves are examined to discuss the goodness of the general density variables used to construct the order parameters.

Section snippets

Experimental

The benzonitrile, mass fraction 0.99, obtained from the Shanghai Kaiming Chemical Factory was distilled slowly under reduced pressure. The middle part of the distillate was collected and stored over a 0.4 nm molecular sieve. The hexadecane, mass fraction 0.99, supplied by Fluka Co., was dried and stored over a 0.4 nm molecular sieve.

The coexistence curves were determined by measurements of the refractive indices n of two coexisting phases using a technique of “minimum deviations” The apparatus

Coexistence curves

The critical mole fraction and the critical temperature of {xC6H5CN + (1  x)CH3(CH2)14CH3} were determined to be xc = (0.673 ± 0.001) and Tc = (304.4 ± 0.2) K, respectively. The refractive indices n were measured for each coexisting phase at various temperatures. The results are listed in columns 2 and 3 of table 1 and are shown in figure 1(a).

In order to obtain the (T, x) coexistence curve, a series of binary mixtures with known mole fractions x was prepared and their refractive indices in the single-

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Projects 20173024, 20273032 and 20473035) and the Key Project of Chinese Ministry of Education (No. 105074).

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